<?php

require_once "../Matrix.php";

/**
 * Given n points (x0,y0)...(xn-1,yn-1), the following methid computes
 * the polynomial factors of the n-1't degree polynomial passing through
 * the n points.
 *
 * Example: Passing in three points (2,3) (1,4) and (3,7) will produce
 * the results [2.5, -8.5, 10] which means that the points are on the
 * curve y = 2.5x² - 8.5x + 10.
 *
 * @see http://geosoft.no/software/lagrange/LagrangeInterpolation.java.html
 * @author Jacob Dreyer
 * @author Paul Meagher (port to PHP and minor changes)
 *
 * @param x[] float
 * @param y[] float
 */
class LagrangeInterpolation {

    public function findPolynomialFactors($x, $y) {
        $n = count($x);

        $data = array();  // double[n][n];
        $rhs  = array();  // double[n];

        for ($i = 0; $i < $n; ++$i) {
            $v = 1;
            for ($j = 0; $j < $n; ++$j) {
                $data[$i][$n-$j-1] = $v;
                $v *= $x[$i];
            }
            $rhs[$i] = $y[$i];
        }

        // Solve m * s = b
        $m = new Matrix($data);
        $b = new Matrix($rhs, $n);

        $s = $m->solve($b);

        return $s->getRowPackedCopy();
    }    //    function findPolynomialFactors()

}    //    class LagrangeInterpolation


$x = array(2.0, 1.0, 3.0);
$y = array(3.0, 4.0, 7.0);

$li = new LagrangeInterpolation;
$f = $li->findPolynomialFactors($x, $y);


for ($i = 0; $i < 3; ++$i) {
    echo $f[$i]."<br />";
}
